1 Intention

The goal of this document is to calculate the growth rate (r) and the carrying capacity (K) of 6 species of ciliates that we grew individually in a replicated (n = 3) factorial experiment with 5 temperatures (18, 21, 24, 26, and 28), 5 nutrients levels and their combinations (= 25 treatments) for 3 weeks. The calculated r and K are then going to be used as the traits to calculate potential response diversity of communities composed of 2, 3, and 4 species to all possible changes in temperature and nutrients. The calculated potential response diversity will inform us on which communities will be used in the following experimental step. We are going to calculate the growth rate as the slope of the regression of ln(Nt) where: ln is natural log and Nt is the population density at time t, during the period of exponential growth. We are going to set initially the period of exponential growth as the first 6 days, but we are going to visually check whether this choice is correct. K will be calculated as the highest population biomass for each population during the experiment.

Let’s start loading the data set and creating a subset for calculating r

Time series of species densities across the treatments.

(#fig:time_series_spp)Time series of species densities across the treatments.

1.1 Calculate K and r

## # A tibble: 6 × 7
##   species   nutrients temperature sample_ID Intercept GrowthRate RSquared
##   <chr>         <int>       <int> <chr>         <dbl>      <dbl>    <dbl>
## 1 Colpidium         1          18 C1             5.43   -0.0285   0.0113 
## 2 Colpidium         1          18 C2             5.06    0.135    0.510  
## 3 Colpidium         1          18 C3             5.43   -0.00431  0.00466
## 4 Colpidium         1          21 C16            5.08    0.0609   0.166  
## 5 Colpidium         1          21 C17            5.98   -0.125    0.601  
## 6 Colpidium         1          21 C18            4.84    0.0102   0.0864

Visual inspection of exponential growth phase

Species densities across the treatments with the regression lines used to calculate the intrinsic rate of growth (r).

(#fig:reg_all)Species densities across the treatments with the regression lines used to calculate the intrinsic rate of growth (r).

1.2 GAMs to fit responde surface

At least for now, we focus on the intrinsic rate of growth (r). We are going to fit response surfaces using the calculated r for all species using GAMs. Then we are also going to use r as the species’ trait to calculate potential response diversity, as well as response diversity when the direction of the environmental change is known. The rationale is that r is likely of more relevance if the environmental change of interest occurs rapidly, since r provides information on a population’s ability to rapidly bounce back after disturbance. In the upcoming experiment, we will have temperature fluctuating relatively fast, and so we decide now to focus on r.

Use GAMs to fit response surface of r and K

species temperature nutrients  predicted

1 Colpidium 18 1.00 0.02209644 2 Colpidium 18 1.01 0.02847381 3 Colpidium 18 1.02 0.03485059 4 Colpidium 18 1.03 0.04122618 5 Colpidium 18 1.04 0.04759996 6 Colpidium 18 1.05 0.05397136

Create surface plots

We now check how the GAMs surfaces (r) look compared to the measured densities.

Checking predictions
Measured density values of Dexiostoma in the different treatments (a) vs fitted surface of growth rate (b).

(#fig:surface_Dexi)Measured density values of Dexiostoma in the different treatments (a) vs fitted surface of growth rate (b).

Measured density values of Colpidium in the different treatments (a) vs fitted surface of growth rate (b).

(#fig:surface_colp)Measured density values of Colpidium in the different treatments (a) vs fitted surface of growth rate (b).

Measured density values of Loxocephalus in the different treatments (a) vs fitted surface of growth rate (b).

(#fig:surface_loxo)Measured density values of Loxocephalus in the different treatments (a) vs fitted surface of growth rate (b).

Measured density values of Paramecium in the different treatments (a) vs fitted surface of growth rate (b).

(#fig:surface_paramecium)Measured density values of Paramecium in the different treatments (a) vs fitted surface of growth rate (b).

Measured density values of Spirostotum in the different treatments (a) vs fitted surface of growth rate (b).

(#fig:surface_spiro)Measured density values of Spirostotum in the different treatments (a) vs fitted surface of growth rate (b).

Measured density values of Tetrahymena in the different treatments (a) vs fitted surface of growth rate (b).

(#fig:surface_tetra)Measured density values of Tetrahymena in the different treatments (a) vs fitted surface of growth rate (b).

2 Calculate Potential Response diversity

After discussion, we decided to remove Tetrahymena

Now, we calculate potential response diversity for all possible communities composed of 2, 3, and 4 species. We start with all communities composed of 2 species.

2.1 Potential response diversity 2 species communities

Steps are:

  • Create ref environmental conditions

  • Create all possible communities with 2 species

  • Calculate potential response diversity for all communities richness = 2 with our function “get_potential_RD”

Results divergence dissimilarity species composition richness 1 0.1588557 1.030525 Colpidium_Dexiostoma CD 2 2 0.2335566 1.071145 Colpidium_Loxocephalus CL 2 3 0.2181896 1.084048 Colpidium_Paramecium CP 2 4 0.1674162 1.031427 Colpidium_Spirostomum CS 2 5 0.1888952 1.061412 Dexiostoma_Loxocephalus DL 2 6 0.1793463 1.068837 Dexiostoma_Paramecium DP 2

2.2 Potential Response Diversity 3 species communities

Results divergence dissimilarity species composition 1 0.2909493 1.073725 Colpidium_Dexiostoma_Loxocephalus CDL 2 0.2738953 1.084341 Colpidium_Dexiostoma_Paramecium CDP 3 0.2565149 1.037684 Colpidium_Dexiostoma_Spirostomum CDS 4 0.3670888 1.114132 Colpidium_Loxocephalus_Paramecium CLP 5 0.3118829 1.074970 Colpidium_Loxocephalus_Spirostomum CLS 6 0.2733158 1.082258 Colpidium_Paramecium_Spirostomum CPS richness 1 3 2 3 3 3 4 3 5 3 6 3

2.3 Potential Response Diversity 4 species communities

Results

divergence dissimilarity species 1 0.3891995 1.107493 Colpidium_Dexiostoma_Loxocephalus_Paramecium 2 0.3451865 1.071705 Colpidium_Dexiostoma_Loxocephalus_Spirostomum 3 0.3090725 1.079250 Colpidium_Dexiostoma_Paramecium_Spirostomum 4 0.3855761 1.107105 Colpidium_Loxocephalus_Paramecium_Spirostomum 5 0.3786722 1.098081 Dexiostoma_Loxocephalus_Paramecium_Spirostomum composition richness 1 CDLP 4 2 CDLS 4 3 CDPS 4 4 CLPS 4 5 DLPS 4

Potential Response diversity per species richness measured as dissimilarity (a) and divergence (b).

(#fig:potential_RD_plot)Potential Response diversity per species richness measured as dissimilarity (a) and divergence (b).

3 Response diversity known direction of environmental change

Now we calculate RD with known direction of environmental change, i.e. the ones we are going to apply in the experiment. We are going to calculate response diversity for multiple possible ranges of temperature fluctuations. - Create a data set with environmental conditions that we may use in the experiment and calculate RD knowing the direction of the environmental change.

  • fluctuating temperature x 3 fixed nutrients = 9 treatments

4 First env change scenario

  • first fluctuation ranges are going to be 18-22, 22-26, and 24 - 28
Time series of the environmental conditions for temperature (a) and nutrients (b). These environmental conditions represent the "treatments" and will be crossed in a full factorial design resulting in 9 unique treatments

(#fig:env_sp2_t1)Time series of the environmental conditions for temperature (a) and nutrients (b). These environmental conditions represent the “treatments” and will be crossed in a full factorial design resulting in 9 unique treatments

4.1 Response diversity 2 species communities

Same steps as before:

  • Create all possible communities with 2 species

  • Actual RD calculation

Results time temperature nutrients dissimilarity divergence species 1 0 20 1 1.014285 0.8675564 Colpidium_Dexiostoma 2 0 20 3 1.000146 0.0000000 Colpidium_Dexiostoma 3 0 20 5 1.007525 0.0000000 Colpidium_Dexiostoma 4 0 24 1 1.003775 0.0000000 Colpidium_Dexiostoma 5 0 24 3 1.023785 0.1823538 Colpidium_Dexiostoma 6 0 24 5 1.013883 0.0000000 Colpidium_Dexiostoma composition richness 1 CD 2 2 CD 2 3 CD 2 4 CD 2 5 CD 2 6 CD 2

Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 2 species

(#fig:RD_2sp_t1)Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 2 species

4.2 Response diversity 3 species communities

Now, we calculate RD for all possible communities of 3 species knowing the direction of the environmental change (we created before).

time temperature nutrients dissimilarity divergence 1 0 20 1 1.019938 0.5543975 2 0 20 3 1.000395 0.0000000 3 0 20 5 1.006697 0.0000000 4 0 24 1 1.005815 0.0000000 5 0 24 3 1.021194 0.1823538 6 0 24 5 1.012367 0.0000000 species composition richness 1 Colpidium_Dexiostoma_Loxocephalus CDL 3 2 Colpidium_Dexiostoma_Loxocephalus CDL 3 3 Colpidium_Dexiostoma_Loxocephalus CDL 3 4 Colpidium_Dexiostoma_Loxocephalus CDL 3 5 Colpidium_Dexiostoma_Loxocephalus CDL 3 6 Colpidium_Dexiostoma_Loxocephalus CDL 3

Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 3 species

(#fig:RD_3sp_t1)Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 3 species

4.3 Response diversity 4 species communities

Now, we calculate RD for all possible communities of 4 species knowing the direction of the environmental change (we created before).

time temperature nutrients dissimilarity divergence 1 0 20 1 1.017338 0.5543975 2 0 20 3 1.004367 0.3250017 3 0 20 5 1.028954 0.8517962 4 0 24 1 1.013329 0.5165705 5 0 24 3 1.021602 0.1823538 6 0 24 5 1.067810 0.4329536 species composition richness 1 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4 2 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4 3 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4 4 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4 5 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4 6 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4

Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 4 species

(#fig:RD_4sp_t1)Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 4 species

Summary of Response divergence measured for all possible communities of 2, 3, and 4 species with known direction of environmental change

(#fig:summary_RD_t1)Summary of Response divergence measured for all possible communities of 2, 3, and 4 species with known direction of environmental change

5 Second env scenario

  • first fluctuation ranges are going to be 18-21, 22-25, and 25 - 28
Time series of the environmental conditions for temperature (a) and nutrients (b). These environmental conditions represent the "treatments" and will be crossed in a full factorial design resulting in 9 unique treatments

(#fig:env_scenario2_t2)Time series of the environmental conditions for temperature (a) and nutrients (b). These environmental conditions represent the “treatments” and will be crossed in a full factorial design resulting in 9 unique treatments

5.1 Response diversity 2 species communities

Same steps as before:

  • Create all possible communities with 2 species

  • Actual RD calculation

Results time temperature nutrients dissimilarity divergence species 1 0 20.0 1 1.014285 0.8675564 Colpidium_Dexiostoma 2 0 20.0 3 1.000146 0.0000000 Colpidium_Dexiostoma 3 0 20.0 5 1.007525 0.0000000 Colpidium_Dexiostoma 4 0 23.5 1 1.020179 0.8138174 Colpidium_Dexiostoma 5 0 23.5 3 1.015886 0.6171164 Colpidium_Dexiostoma 6 0 23.5 5 1.003021 0.2372650 Colpidium_Dexiostoma composition richness 1 CD 2 2 CD 2 3 CD 2 4 CD 2 5 CD 2 6 CD 2

Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 2 species

(#fig:RD_2sp_t2)Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 2 species

5.2 Response diversity 3 species communities

Now, we calculate RD for all possible communities of 3 species knowing the direction of the environmental change (we created before).

time temperature nutrients dissimilarity divergence 1 0 20.0 1 1.019938 0.5543975 2 0 20.0 3 1.000395 0.0000000 3 0 20.0 5 1.006697 0.0000000 4 0 23.5 1 1.017989 0.8138174 5 0 23.5 3 1.014131 0.6171164 6 0 23.5 5 1.022391 0.2117644 species composition richness 1 Colpidium_Dexiostoma_Loxocephalus CDL 3 2 Colpidium_Dexiostoma_Loxocephalus CDL 3 3 Colpidium_Dexiostoma_Loxocephalus CDL 3 4 Colpidium_Dexiostoma_Loxocephalus CDL 3 5 Colpidium_Dexiostoma_Loxocephalus CDL 3 6 Colpidium_Dexiostoma_Loxocephalus CDL 3

Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 3 species

(#fig:RD_3sp_t2)Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 3 species

5.3 Response diversity 4 species communities

Now, we calculate RD for all possible communities of 4 species knowing the direction of the environmental change (we created before).

time temperature nutrients dissimilarity divergence 1 0 20.0 1 1.017338 0.5543975 2 0 20.0 3 1.004367 0.3250017 3 0 20.0 5 1.028954 0.8517962 4 0 23.5 1 1.019316 0.7839241 5 0 23.5 3 1.014257 0.6171164 6 0 23.5 5 1.029033 0.7993990 species composition richness 1 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4 2 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4 3 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4 4 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4 5 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4 6 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4

Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 4 species

(#fig:RD_4sp_t2)Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 4 species

Summary of Response divergence measured for all possible communities of 2, 3, and 4 species with known direction of environmental change

(#fig:summary_RD_t2)Summary of Response divergence measured for all possible communities of 2, 3, and 4 species with known direction of environmental change

6 Third env scenario

  • third fluctuation ranges are going to be 18-20, 21-24, and 26 - 28
Time series of the environmental conditions for temperature (a) and nutrients (b). These environmental conditions represent the "treatments" and will be crossed in a full factorial design resulting in 9 unique treatments

(#fig:env_scenario2_t3)Time series of the environmental conditions for temperature (a) and nutrients (b). These environmental conditions represent the “treatments” and will be crossed in a full factorial design resulting in 9 unique treatments

6.1 Response diversity 2 species communities

Same steps as before:

  • Create all possible communities with 2 species

  • Actual RD calculation

Results time temperature nutrients dissimilarity divergence species 1 0 19 1 1.000552 0.0000000 Colpidium_Dexiostoma 2 0 19 3 1.000292 0.0000000 Colpidium_Dexiostoma 3 0 19 5 1.000194 0.0000000 Colpidium_Dexiostoma 4 0 23 1 1.037269 0.4175873 Colpidium_Dexiostoma 5 0 23 3 1.009501 0.5874308 Colpidium_Dexiostoma 6 0 23 5 1.015448 0.0000000 Colpidium_Dexiostoma composition richness 1 CD 2 2 CD 2 3 CD 2 4 CD 2 5 CD 2 6 CD 2

Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 2 species

(#fig:RD_2sp_t3)Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 2 species

6.2 Response diversity 3 species communities

Now, we calculate RD for all possible communities of 3 species knowing the direction of the environmental change (we created before).

time temperature nutrients dissimilarity divergence 1 0 19 1 1.021717 0.4899515 2 0 19 3 1.000790 0.0000000 3 0 19 5 1.015073 0.0000000 4 0 23 1 1.033286 0.4175873 5 0 23 3 1.009627 0.7597807 6 0 23 5 1.041188 0.7607379 species composition richness 1 Colpidium_Dexiostoma_Loxocephalus CDL 3 2 Colpidium_Dexiostoma_Loxocephalus CDL 3 3 Colpidium_Dexiostoma_Loxocephalus CDL 3 4 Colpidium_Dexiostoma_Loxocephalus CDL 3 5 Colpidium_Dexiostoma_Loxocephalus CDL 3 6 Colpidium_Dexiostoma_Loxocephalus CDL 3

Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 3 species

(#fig:RD_3sp_t3)Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 3 species

6.3 Response diversity 4 species communities

Now, we calculate RD for all possible communities of 4 species knowing the direction of the environmental change (we created before).

time temperature nutrients dissimilarity divergence 1 0 19 1 1.021049 0.4899515 2 0 19 3 1.004374 0.0000000 3 0 19 5 1.058813 0.7954759 4 0 23 1 1.032564 0.4175873 5 0 23 3 1.008965 0.7597807 6 0 23 5 1.041181 0.7607379 species composition richness 1 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4 2 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4 3 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4 4 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4 5 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4 6 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4

Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 4 species

(#fig:RD_4sp_t3)Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 4 species

Summary of Response divergence measured for all possible communities of 2, 3, and 4 species with known direction of environmental change

(#fig:summary_RD_t3)Summary of Response divergence measured for all possible communities of 2, 3, and 4 species with known direction of environmental change

7 Changing fluctuating frequency

Seâme temperature fluctuations as before, but now fluctuating over 4 days

  • Create a data set with environmental conditions that we may use in the experiment and calculate RD knowing the direction of the environmental change.

  • fluctuating temperature x 3 fixed nutrients = 9 treatments

8 First env change scenario

  • first fluctuation ranges are going to be 18-22, 22-26, and 24 - 28
Time series of the environmental conditions for temperature (a) and nutrients (b). These environmental conditions represent the "treatments" and will be crossed in a full factorial design resulting in 9 unique treatments

(#fig:env_sp2_T1)Time series of the environmental conditions for temperature (a) and nutrients (b). These environmental conditions represent the “treatments” and will be crossed in a full factorial design resulting in 9 unique treatments

8.1 Response diversity 2 species communities

Same steps as before:

  • Create all possible communities with 2 species

  • Actual RD calculation

Results time temperature nutrients dissimilarity divergence species 1 0 20 1 1.014285 0.8675564 Colpidium_Dexiostoma 2 0 20 3 1.000146 0.0000000 Colpidium_Dexiostoma 3 0 20 5 1.007525 0.0000000 Colpidium_Dexiostoma 4 0 24 1 1.003775 0.0000000 Colpidium_Dexiostoma 5 0 24 3 1.023785 0.1823538 Colpidium_Dexiostoma 6 0 24 5 1.013883 0.0000000 Colpidium_Dexiostoma composition richness 1 CD 2 2 CD 2 3 CD 2 4 CD 2 5 CD 2 6 CD 2

Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 2 species

(#fig:RD_2sp_T1)Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 2 species

8.2 Response diversity 3 species communities

Now, we calculate RD for all possible communities of 3 species knowing the direction of the environmental change (we created before).

time temperature nutrients dissimilarity divergence 1 0 20 1 1.019938 0.5543975 2 0 20 3 1.000395 0.0000000 3 0 20 5 1.006697 0.0000000 4 0 24 1 1.005815 0.0000000 5 0 24 3 1.021194 0.1823538 6 0 24 5 1.012367 0.0000000 species composition richness 1 Colpidium_Dexiostoma_Loxocephalus CDL 3 2 Colpidium_Dexiostoma_Loxocephalus CDL 3 3 Colpidium_Dexiostoma_Loxocephalus CDL 3 4 Colpidium_Dexiostoma_Loxocephalus CDL 3 5 Colpidium_Dexiostoma_Loxocephalus CDL 3 6 Colpidium_Dexiostoma_Loxocephalus CDL 3

Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 3 species

(#fig:RD_3sp_T1)Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 3 species

8.3 Response diversity 4 species communities

Now, we calculate RD for all possible communities of 4 species knowing the direction of the environmental change (we created before).

time temperature nutrients dissimilarity divergence 1 0 20 1 1.017338 0.5543975 2 0 20 3 1.004367 0.3250017 3 0 20 5 1.028954 0.8517962 4 0 24 1 1.013329 0.5165705 5 0 24 3 1.021602 0.1823538 6 0 24 5 1.067810 0.4329536 species composition richness 1 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4 2 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4 3 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4 4 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4 5 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4 6 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4

Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 4 species

(#fig:RD_4sp_T1)Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 4 species

Summary of Response divergence measured for all possible communities of 2, 3, and 4 species with known direction of environmental change

(#fig:summary_RD_T1)Summary of Response divergence measured for all possible communities of 2, 3, and 4 species with known direction of environmental change

9 Second env scenario

  • first fluctuation ranges are going to be 18-21, 22-25, and 25 - 28
Time series of the environmental conditions for temperature (a) and nutrients (b). These environmental conditions represent the "treatments" and will be crossed in a full factorial design resulting in 9 unique treatments

(#fig:env_scenario2_T2)Time series of the environmental conditions for temperature (a) and nutrients (b). These environmental conditions represent the “treatments” and will be crossed in a full factorial design resulting in 9 unique treatments

9.1 Response diversity 2 species communities

Same steps as before:

  • Create all possible communities with 2 species

  • Actual RD calculation

Results time temperature nutrients dissimilarity divergence species 1 0 20.0 1 1.014285 0.8675564 Colpidium_Dexiostoma 2 0 20.0 3 1.000146 0.0000000 Colpidium_Dexiostoma 3 0 20.0 5 1.007525 0.0000000 Colpidium_Dexiostoma 4 0 23.5 1 1.020179 0.8138174 Colpidium_Dexiostoma 5 0 23.5 3 1.015886 0.6171164 Colpidium_Dexiostoma 6 0 23.5 5 1.003021 0.2372650 Colpidium_Dexiostoma composition richness 1 CD 2 2 CD 2 3 CD 2 4 CD 2 5 CD 2 6 CD 2

Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 2 species

(#fig:RD_2sp_T2)Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 2 species

9.2 Response diversity 3 species communities

Now, we calculate RD for all possible communities of 3 species knowing the direction of the environmental change (we created before).

time temperature nutrients dissimilarity divergence 1 0 20.0 1 1.019938 0.5543975 2 0 20.0 3 1.000395 0.0000000 3 0 20.0 5 1.006697 0.0000000 4 0 23.5 1 1.017989 0.8138174 5 0 23.5 3 1.014131 0.6171164 6 0 23.5 5 1.022391 0.2117644 species composition richness 1 Colpidium_Dexiostoma_Loxocephalus CDL 3 2 Colpidium_Dexiostoma_Loxocephalus CDL 3 3 Colpidium_Dexiostoma_Loxocephalus CDL 3 4 Colpidium_Dexiostoma_Loxocephalus CDL 3 5 Colpidium_Dexiostoma_Loxocephalus CDL 3 6 Colpidium_Dexiostoma_Loxocephalus CDL 3

Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 3 species

(#fig:RD_3sp_T2)Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 3 species

9.3 Response diversity 4 species communities

Now, we calculate RD for all possible communities of 4 species knowing the direction of the environmental change (we created before).

time temperature nutrients dissimilarity divergence 1 0 20.0 1 1.017338 0.5543975 2 0 20.0 3 1.004367 0.3250017 3 0 20.0 5 1.028954 0.8517962 4 0 23.5 1 1.019316 0.7839241 5 0 23.5 3 1.014257 0.6171164 6 0 23.5 5 1.029033 0.7993990 species composition richness 1 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4 2 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4 3 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4 4 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4 5 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4 6 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4

Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 4 species

(#fig:RD_4sp_T2)Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 4 species

Summary of Response divergence measured for all possible communities of 2, 3, and 4 species with known direction of environmental change

(#fig:summary_RD_T2)Summary of Response divergence measured for all possible communities of 2, 3, and 4 species with known direction of environmental change

10 Third env scenario

  • third fluctuation ranges are going to be 18-20, 21-24, and 26 - 28
Time series of the environmental conditions for temperature (a) and nutrients (b). These environmental conditions represent the "treatments" and will be crossed in a full factorial design resulting in 9 unique treatments

(#fig:env_scenario2_T3)Time series of the environmental conditions for temperature (a) and nutrients (b). These environmental conditions represent the “treatments” and will be crossed in a full factorial design resulting in 9 unique treatments

10.1 Response diversity 2 species communities

Same steps as before:

  • Create all possible communities with 2 species

  • Actual RD calculation

Results time temperature nutrients dissimilarity divergence species 1 0 19 1 1.000552 0.0000000 Colpidium_Dexiostoma 2 0 19 3 1.000292 0.0000000 Colpidium_Dexiostoma 3 0 19 5 1.000194 0.0000000 Colpidium_Dexiostoma 4 0 23 1 1.037269 0.4175873 Colpidium_Dexiostoma 5 0 23 3 1.009501 0.5874308 Colpidium_Dexiostoma 6 0 23 5 1.015448 0.0000000 Colpidium_Dexiostoma composition richness 1 CD 2 2 CD 2 3 CD 2 4 CD 2 5 CD 2 6 CD 2

Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 2 species

(#fig:RD_2sp_T3)Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 2 species

10.2 Response diversity 3 species communities

Now, we calculate RD for all possible communities of 3 species knowing the direction of the environmental change (we created before).

time temperature nutrients dissimilarity divergence 1 0 19 1 1.021717 0.4899515 2 0 19 3 1.000790 0.0000000 3 0 19 5 1.015073 0.0000000 4 0 23 1 1.033286 0.4175873 5 0 23 3 1.009627 0.7597807 6 0 23 5 1.041188 0.7607379 species composition richness 1 Colpidium_Dexiostoma_Loxocephalus CDL 3 2 Colpidium_Dexiostoma_Loxocephalus CDL 3 3 Colpidium_Dexiostoma_Loxocephalus CDL 3 4 Colpidium_Dexiostoma_Loxocephalus CDL 3 5 Colpidium_Dexiostoma_Loxocephalus CDL 3 6 Colpidium_Dexiostoma_Loxocephalus CDL 3

Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 3 species

(#fig:RD_3sp_T3)Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 3 species

10.3 Response diversity 4 species communities

Now, we calculate RD for all possible communities of 4 species knowing the direction of the environmental change (we created before).

time temperature nutrients dissimilarity divergence 1 0 19 1 1.021049 0.4899515 2 0 19 3 1.004374 0.0000000 3 0 19 5 1.058813 0.7954759 4 0 23 1 1.032564 0.4175873 5 0 23 3 1.008965 0.7597807 6 0 23 5 1.041181 0.7607379 species composition richness 1 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4 2 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4 3 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4 4 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4 5 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4 6 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4

Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 4 species

(#fig:RD_4sp_T3)Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 4 species

Summary of Response divergence measured for all possible communities of 2, 3, and 4 species with known direction of environmental change

(#fig:summary_RD_T3)Summary of Response divergence measured for all possible communities of 2, 3, and 4 species with known direction of environmental change

11 Changing nutrients

Same temperature fluctuations as before, different nutrient levels

  • Create a data set with environmental conditions that we may use in the experiment and calculate RD knowing the direction of the environmental change.

  • fluctuating temperature x 3 fixed nutrients = 9 treatments

12 First env change scenario

  • first fluctuation ranges are going to be 18-22, 22-26, and 24 - 28
Time series of the environmental conditions for temperature (a) and nutrients (b). These environmental conditions represent the "treatments" and will be crossed in a full factorial design resulting in 9 unique treatments

(#fig:env_sp2_nut)Time series of the environmental conditions for temperature (a) and nutrients (b). These environmental conditions represent the “treatments” and will be crossed in a full factorial design resulting in 9 unique treatments

12.1 Response diversity 2 species communities

Same steps as before:

  • Create all possible communities with 2 species

  • Actual RD calculation

Results time temperature nutrients dissimilarity divergence species 1 0 20 1 1.014285 0.8675564 Colpidium_Dexiostoma 2 0 20 2 1.000626 0.0000000 Colpidium_Dexiostoma 3 0 20 4 1.000216 0.0000000 Colpidium_Dexiostoma 4 0 24 1 1.003775 0.0000000 Colpidium_Dexiostoma 5 0 24 2 1.004169 0.0000000 Colpidium_Dexiostoma 6 0 24 4 1.020227 0.5027382 Colpidium_Dexiostoma composition richness 1 CD 2 2 CD 2 3 CD 2 4 CD 2 5 CD 2 6 CD 2

Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 2 species

(#fig:RD_2sp_nut1)Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 2 species

12.2 Response diversity 3 species communities

Now, we calculate RD for all possible communities of 3 species knowing the direction of the environmental change (we created before).

time temperature nutrients dissimilarity divergence 1 0 20 1 1.019938 0.5543975 2 0 20 2 1.012601 0.4411389 3 0 20 4 1.025028 0.6926586 4 0 24 1 1.005815 0.0000000 5 0 24 2 1.003708 0.0000000 6 0 24 4 1.033319 0.2729436 species composition richness 1 Colpidium_Dexiostoma_Loxocephalus CDL 3 2 Colpidium_Dexiostoma_Loxocephalus CDL 3 3 Colpidium_Dexiostoma_Loxocephalus CDL 3 4 Colpidium_Dexiostoma_Loxocephalus CDL 3 5 Colpidium_Dexiostoma_Loxocephalus CDL 3 6 Colpidium_Dexiostoma_Loxocephalus CDL 3

Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 3 species

(#fig:RD_3sp_nut1)Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 3 species

12.3 Response diversity 4 species communities

Now, we calculate RD for all possible communities of 4 species knowing the direction of the environmental change (we created before).

time temperature nutrients dissimilarity divergence 1 0 20 1 1.017338 0.5543975 2 0 20 2 1.042587 0.3931826 3 0 20 4 1.028192 0.9856921 4 0 24 1 1.013329 0.5165705 5 0 24 2 1.025079 0.9044590 6 0 24 4 1.029328 0.2729436 species composition richness 1 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4 2 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4 3 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4 4 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4 5 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4 6 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4

Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 4 species

(#fig:RD_4sp_nut1)Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 4 species

Summary of Response divergence measured for all possible communities of 2, 3, and 4 species with known direction of environmental change

(#fig:summary_RD_nut1)Summary of Response divergence measured for all possible communities of 2, 3, and 4 species with known direction of environmental change

13 Second env scenario

  • first fluctuation ranges are going to be 18-21, 22-25, and 25 - 28
Time series of the environmental conditions for temperature (a) and nutrients (b). These environmental conditions represent the "treatments" and will be crossed in a full factorial design resulting in 9 unique treatments

(#fig:env_scenario2_nut)Time series of the environmental conditions for temperature (a) and nutrients (b). These environmental conditions represent the “treatments” and will be crossed in a full factorial design resulting in 9 unique treatments

13.1 Response diversity 2 species communities

Same steps as before:

  • Create all possible communities with 2 species

  • Actual RD calculation

Results time temperature nutrients dissimilarity divergence species 1 0 20.0 1 1.014285 0.8675564 Colpidium_Dexiostoma 2 0 20.0 2 1.000626 0.0000000 Colpidium_Dexiostoma 3 0 20.0 4 1.000216 0.0000000 Colpidium_Dexiostoma 4 0 23.5 1 1.020179 0.8138174 Colpidium_Dexiostoma 5 0 23.5 2 1.001249 0.0000000 Colpidium_Dexiostoma 6 0 23.5 4 1.011091 0.1753557 Colpidium_Dexiostoma composition richness 1 CD 2 2 CD 2 3 CD 2 4 CD 2 5 CD 2 6 CD 2

Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 2 species

(#fig:RD_2sp_nut)Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 2 species

13.2 Response diversity 3 species communities

Now, we calculate RD for all possible communities of 3 species knowing the direction of the environmental change (we created before).

time temperature nutrients dissimilarity divergence 1 0 20.0 1 1.019938 0.55439751 2 0 20.0 2 1.012601 0.44113888 3 0 20.0 4 1.025028 0.69265863 4 0 23.5 1 1.017989 0.81381739 5 0 23.5 2 1.012359 0.00000000 6 0 23.5 4 1.032834 0.05291428 species composition richness 1 Colpidium_Dexiostoma_Loxocephalus CDL 3 2 Colpidium_Dexiostoma_Loxocephalus CDL 3 3 Colpidium_Dexiostoma_Loxocephalus CDL 3 4 Colpidium_Dexiostoma_Loxocephalus CDL 3 5 Colpidium_Dexiostoma_Loxocephalus CDL 3 6 Colpidium_Dexiostoma_Loxocephalus CDL 3

Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 3 species

(#fig:RD_3sp_nut)Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 3 species

13.3 Response diversity 4 species communities

Now, we calculate RD for all possible communities of 4 species knowing the direction of the environmental change (we created before).

time temperature nutrients dissimilarity divergence 1 0 20.0 1 1.017338 0.55439751 2 0 20.0 2 1.042587 0.39318257 3 0 20.0 4 1.028192 0.98569214 4 0 23.5 1 1.019316 0.78392411 5 0 23.5 2 1.022494 0.89912806 6 0 23.5 4 1.030460 0.05291428 species composition richness 1 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4 2 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4 3 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4 4 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4 5 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4 6 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4

Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 4 species

(#fig:RD_4sp_nut)Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 4 species

Summary of Response divergence measured for all possible communities of 2, 3, and 4 species with known direction of environmental change

(#fig:summary_RD_nut)Summary of Response divergence measured for all possible communities of 2, 3, and 4 species with known direction of environmental change

14 Third env scenario

  • third fluctuation ranges are going to be 18-20, 21-24, and 26 - 28
Time series of the environmental conditions for temperature (a) and nutrients (b). These environmental conditions represent the "treatments" and will be crossed in a full factorial design resulting in 9 unique treatments

(#fig:env_scenario3_nut)Time series of the environmental conditions for temperature (a) and nutrients (b). These environmental conditions represent the “treatments” and will be crossed in a full factorial design resulting in 9 unique treatments

14.1 Response diversity 2 species communities

Same steps as before:

  • Create all possible communities with 2 species

  • Actual RD calculation

Results time temperature nutrients dissimilarity divergence species 1 0 19 1 1.000552 0.0000000 Colpidium_Dexiostoma 2 0 19 2 1.001994 0.0000000 Colpidium_Dexiostoma 3 0 19 4 1.001938 0.0000000 Colpidium_Dexiostoma 4 0 23 1 1.037269 0.4175873 Colpidium_Dexiostoma 5 0 23 2 1.000891 0.0000000 Colpidium_Dexiostoma 6 0 23 4 1.004006 0.0000000 Colpidium_Dexiostoma composition richness 1 CD 2 2 CD 2 3 CD 2 4 CD 2 5 CD 2 6 CD 2

Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 2 species

(#fig:RD_2sp_nut3)Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 2 species

14.2 Response diversity 3 species communities

Now, we calculate RD for all possible communities of 3 species knowing the direction of the environmental change (we created before).

time temperature nutrients dissimilarity divergence 1 0 19 1 1.021717 0.4899515 2 0 19 2 1.024758 0.6341672 3 0 19 4 1.023311 0.9607643 4 0 23 1 1.033286 0.4175873 5 0 23 2 1.019656 0.4141403 6 0 23 4 1.032091 0.0000000 species composition richness 1 Colpidium_Dexiostoma_Loxocephalus CDL 3 2 Colpidium_Dexiostoma_Loxocephalus CDL 3 3 Colpidium_Dexiostoma_Loxocephalus CDL 3 4 Colpidium_Dexiostoma_Loxocephalus CDL 3 5 Colpidium_Dexiostoma_Loxocephalus CDL 3 6 Colpidium_Dexiostoma_Loxocephalus CDL 3

Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 3 species

(#fig:RD_3sp_nut3)Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 3 species

14.3 Response diversity 4 species communities

Now, we calculate RD for all possible communities of 4 species knowing the direction of the environmental change (we created before).

time temperature nutrients dissimilarity divergence 1 0 19 1 1.021049 0.4899515 2 0 19 2 1.057423 0.5065171 3 0 19 4 1.035214 0.5478882 4 0 23 1 1.032564 0.4175873 5 0 23 2 1.018996 0.5967009 6 0 23 4 1.032450 0.0000000 species composition richness 1 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4 2 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4 3 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4 4 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4 5 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4 6 Colpidium_Dexiostoma_Loxocephalus_Paramecium CDLP 4

Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 4 species

(#fig:RD_4sp_nut3)Response diversity calcualted as dissimilarity (a) and diversity (b) of communities composed of all possible combinations of 4 species

Summary of Response divergence measured for all possible communities of 2, 3, and 4 species with known direction of environmental change

(#fig:summary_RD_nut3)Summary of Response divergence measured for all possible communities of 2, 3, and 4 species with known direction of environmental change